function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta

h = sigmoid(X * theta); % h is a vector of size m*1

J_reg = lambda * sum(theta(2:end).^2) / (2*m);
J = -(y' * log(h) + (1 - y)' * log(1 - h)) / m + J_reg;

theta0 = theta; theta0(1) = 0;
grad = X' * (h - y) / m + lambda * theta0 / m;


% =============================================================

end
